一种基于CR理论的大柔性机翼非线性气动弹性求解方法

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摘要大展弦比大柔性机翼在气动载荷的作用下，产生较大的弹性变形，其惯性特性、刚度特性、动气动弹性特性等亦发生较大改变，常规的线性气动弹性分析方法不再适用。基于Co-rotational(CR)理论，推导了机翼变形后的切线刚度矩阵和质量矩阵，建立了考虑几何非线性效应的大柔性机翼结构动力学模型；耦合改进的ONERA非线性非定常气动力模型，提出了一种适用于大柔性机翼的非线性气动弹性求解方法。采用Newmark直接数值积分法及松耦合技术在时域内对气动弹性运动方程进行求解，对所提出的非线性气动弹性求解方法的正确性和精度进行了验证，并研究了大柔性机翼的极限环颤振特性。研究表明：适用于大柔性机翼完整的非线性气动弹性建模需要考虑机翼结构大变形和非定常气动力动态失速等非线性因素；弯曲变形可降低临界极限环颤振速度的15%以上，而前移弹性轴能够有效的提高临界极限环颤振速度；所提出的非线性气动弹性求解方法具有较好的精度和效率，满足大柔性机翼非线性气动弹性的求解需求。

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	王伟1
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关键词 ：非线性气动弹性, 极限环颤振, CR理论, 非定常气动力, 动态失速, Newmark积分法

Abstract：Very flexible wings under aerodynamic loads tend to produce large deformation, which result in significant changes in inertial and stiffness characteristics as well as in dynamic aeroelastic response, and the linear aeroelastic model no longer applicable. Based on co-rotational(CR) theory, the tangent stiff matrix and mass matrix are derived, and the dynamical equilibrium equations of geometrically nonlinear structures of space beam elements are established in this paper. Coupling ONERA dynamic stall model, an efficient method of solving nonlinear aeroelasticy of very flexible wings is proposed. Using newmark direct integration method and loose coupled algorithms, a numerical procedure for solving nonlinear aeroelastic governing equations is presented, and the efficiency and precision of the method was proved through a test case. The results and their analysis show preliminary that: structural and aerodynamic nonlinearities should be considered for complete nonlinear dynamic aeroelastic simulations of very flexible wings; the critical limit cycle oscillation speed will decreases by 15% or more due to bending deformation of the wing, but will improved by translating elastic axis; the proposed method of solving nonlinear aeroelastic problems show a good precision and efficiency, and satisfied requirements of nonlinear aeroelastic analysis of very flexible wings.

Key words： nonlinear aeroelasticity limit cycle oscillation CR theory unsteady aerodynamics dynamic stall newmark integration method

收稿日期: 2014-11-25 出版日期: 2015-10-15

引用本文:

王伟1,周洲1，祝小平2，王睿1. 一种基于CR理论的大柔性机翼非线性气动弹性求解方法[J]. 振动与冲击, 2015, 34(19): 62-70.
WANG Wei 1，ZHOU Zhou 1，ZHU Xiao-ping 2，WANG Rui 1 . CO-ROTATIONAL APPROACH OF SOLVING NONLINEAR AEROELASTICY OF VERY FLEXIBLE WINGS. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(19): 62-70.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I19/62

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